⇒ 3x^2 4 gt;2x^2 3x ⇒ 3x^2 4 2x^2+3x gt;0 ⇒x^2+3x 4 gt;0 ⇒x^2+4x x 4 gt;0 ⇒ x(x+4) 1(x+4) gt;0 ⇒(x+4)(x 1) gt;0 ∴ ...

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Addition and Subtraction of Algebraic Expression

Solve: 3x 2 ...

Question

Solve:
${3 x}^{2} - 4 > x (2 x - 3)$

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Solution

$\Rightarrow 3 x^{2} - 4 > 2 x^{2} - 3 x$
$\Rightarrow 3 x^{2} - 4 - 2 x^{2} + 3 x > 0$
$\Rightarrow x^{2} + 3 x - 4 > 0$
$\Rightarrow x^{2} + 4 x - x - 4 > 0$
$\Rightarrow x (x + 4) - 1 (x + 4) > 0$
$\Rightarrow (x + 4) (x - 1) > 0$
$∴ x \in (- \infty, - 4) \cup (1, \infty)$

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